We describe a simple undergraduate lab in which students determine how the
force between two magnetic dipoles depends on their separation. We
consider the case where both dipoles are permanent and the case where one
of the dipoles is induced by the field of the other (permanent) dipole.
Agreement with theoretically expected results is quite good.

Flash-cooling and annealing of macromolecular crystals
have been investigated using in situ X-ray imaging, diffraction-peak
lineshape measurements and conventional crystallographic diffraction.
The dominant mechanisms by which flash-cooling creates disorder are suggested
and a fixed-temperature annealing protocol for reducing this disorder
is demonstrated that should be more reliable and flexible than existing
protocols. Flash-cooling tetragonal lysozyme crystals degrades diffraction
resolution and broadens the distributions of lattice orientations (mosaicity)
and lattice spacings. The diffraction resolution strongly correlates with
the width of the lattice-spacing distribution. Annealing at fixed temperatures
of 253 and 233 K consistently reduces the lattice-spacing spread and improves
the resolution for annealing times up to similar to 30 s. X-ray images
show that this improvement arises from the formation of well ordered domains
with characteristic sizes >10 mm and narrower
mosaicities than the crystal as a whole. Flash-cooled triclinic crystals
of lysozyme, which have a smaller water content than the tetragonal form,
diffract to higher resolution with smaller mosaicities and exhibit pronounced
ordered domain structure even before annealing. It is suggested that differential
thermal expansion of the protein lattice and solvent may be the primary
cause of flash-cooling-induced disorder. Mechanisms by which annealing at
T << 273 K reduce this disorder are discussed.

Measuring the elastic properties
of protein crystals by Brillouin scattering

The dynamic response of tetragonal lysozyme crystals
to dehydration has been characterized in situ using a combination of
X-ray topography, high-resolution diffraction lineshape measurements and
conventional crystallographic diffraction. For dehydration from 98% relative
humidity (r.h.) to above 89%, mosaicity and diffraction resolution show
little change and X-ray topographs remain featureless. Lattice constants
decrease rapidly but the lattice-constant distribution within the crystal
remains very narrow, indicating that water concentration gradients remain
very small. Near 88% r.h., the c-axis lattice parameter decreases abruptly,
the steady-state mosaicity and diffraction resolution degrade sharply and
topographs develop extensive contrast. This transformation exhibits metastability
and hysteresis. At fixed r.h. < 88% it is irreversible, but the original
order can be almost completely restored by rehydration. These results suggest
that this transformation is a first-order structural transition involving
an abrupt loss of crystal water. The front between transformed and untransformed
regions may propagate inward from the crystal surface and the resulting
stresses along the front may degrade mosaicity. Differences in crystal size,
shape and initial perfection may produce the observed variations in degradation
timescale. Consequently, the success of more general post-growth treatments
may often involve identifying procedures that either avoid lattice transitions,
minimize disorder created during such transitions or maintain the lattice
in an ordered metastable state.

Evidence for dipole surface orientational
order at critical interfaces

A. Mukhopadhyay, C. L. Caylor, and
B.M. Law

Physical Review E 61 R1036
(2000)

At the critical interface of dipolar systems, theory predicts that the
amplitude of the surface orientational order α2(z)
~ m*4d2v(z)/dz2,
where m* is a reduced dipole moment and v(z) is the
local composition z within the interface. We find quantitative
agreement with these predictions for two different critical binary liquid
mixtures composed of a highly polar and a nonpolar component.

The mechanisms by which macromolecular impurities degrade the diffraction
properties of protein crystals have been investigated using X-ray topography,
high-resolution diffraction line shape measurements, crystallographic
data collection, chemical analysis, and two-photon excitation fluorescence
microscopy. Hen egg-white lysozyme crystals grown from solutions containing
a structurally unrelated protein (ovotransferrin) and a related protein
(turkey egg-white lysozyme) can exhibit significantly broadened mosaicity
due to formation of cracks and dislocations but have overall B factors
and diffraction resolutions comparable to those of crystals grown from
uncontaminated lysozyme. Direct fluorescence imaging of the three-dimensional
impurity distribution shows that impurities incorporate with different
densities in sectors formed by growth on different crystal faces, and that
impurity densities in the crystal core and along boundaries between growth
sectors can be much larger than in other parts of the crystal. These nonuniformities
create stresses that drive formation of the defects responsible for the mosaic
broadening. Our results provide a rationale for the use of seeding to obtain
high-quality crystals from heavily contaminated solutions and have implications
for the use of crystallization for protein purification.

Macromolecular impurities present in solution have profound effects on
the growth and quality of protein crystals used for x-ray structure
determinations. We have imaged the three-dimensional distribution
of ovotransferrin impurities in crystals of the protein hen egg white
lysozyme (HEWL) using two-photon excitation fluorescence microscopy.
Impurity concentrations differ between the two types of growth sectors
present in tetragonal HEWL crystals and impurities preferentially incorporate
along the boundaries between growth sectors. Cracked crystals show
large impurity-rich cores that are not observed in uncracked crystals.
These nonuniform impurity distributions provide insight into how and why
impurities affect crystal quality. Our results have implications
for crystal growth and for protein purification.

Protein crystals contain many kinds of disorder, but only a small fraction
of these are likely to be important in limiting the diffraction properties
of interest to crystallographers. X-ray topography, high-angular-resolution
reciprocal space measurements, and standard crystallographic data collection
have been used to probe three factors that may produce diffraction-limiting
disorder: (1) solution variations during crystal growth, (2) macromolecular
impurities, and (3) post-growth crystal treatments. Variations
in solution conditions that occur in widely used growth methods may lead
to variations in equilibrium protein conformation and crystal packing as
a crystal grows, and these may induce appreciable disorder for sensitive
proteins. Tetragonal lysozyme crystals subjected to abrupt changes
in temperature, pH, or salt concentration during growth show increased disorder,
consistent with this mechanism. Macromolecular impurities can have profound
effects on protein crystal quality. A combination of diffraction measurements
provides insight into the mechanisms by which particular impurities create
disorder, and this insight leads to a simple approach for reducing this
disorder. Substantial degradation of diffraction properties due
to conformation and lattice constant changes can occur during post-growth
crystal treatments such as heavy-atom compound and drug binding.
Measurements of the time evolution of crystal disorder during controlled
crystal dehydration--a simple model for such treatments--suggest that structural
metastability conferred by the constraints of the crystal lattice plays an
important role in determining the extent to which the diffraction properties
degrade.

Ellipsometric measurements at the liquid-liquid interface of a critical
ionic Ising mixture yield a decrease in the ellipticity ρ̅ as the reduced
temperature t is decreased (for
t > 0.002) in contrast to a
tβ-ν power-law divergence
found for nonionic Ising mixtures. From this surprising result we infer
the existence of an anisotropic interface. A model of such an interface
is used to calculate theoretical ρ̅ data, which capture some of the characteristics
of the experimental results.

The scaling behavior of critical
adsorption in critical polymer solutions

C. L. Caylor and B. M. Law

Journal of Chemical Physics 104
2070 (1996)

Thecritical adsorption ellipsometric measurements of five
solutions of polystyrene incyclohexane for different polystyrene
molecular weights collapse to a singleuniversal curve when
scaled as a function of nBξ
/λ , wherenB
is the polymer solution refractive index, ξ = ξ 0N
nt–ν is thecorrelation
length, and λ is the wavelength of incident lightin vacuum.
From this universal feature we deduce the valueof the polymerization
critical exponent n = 0.258 ± 0.017. We consider both thevolume fraction order parameter (φ) and a symmetrized order parameter(ψs) together with both the renormalization group
(RG) and MonteCarlo (MC) simulation forms for the surface scaling
function P + (x).The symmetrized
order parameter gives significantly better agreement with experimentthan the volume fraction order parameter. The combination of RGand ψs provides better agreement with experiment
than does thecombination of MC and ψs.